Yes, I found the picture on a royal blog and the caption underneath read 'A young Princess Eugenie curtseying to the Queen Mother'- or something similar.

__________________"She is a little angel and like her name, she brings sunshine even on cloudy days. From the bottom of our hearts, we would like to thank each and every one of you for your lovely best wishes for our daughter. She feels very loved". HRH Princess Madeleine, Duchess of Hälsingland and Gästrikland on her daughter, HRH Princess Leonore, Duchess of Gotland.

I see it's a matter of choice when making these curtseys to bow your head, as Sophie did, or look directly at the person.

I once read that back in the '50s and '60s the rumour was that the Duke of Edinburgh would smile at you when you curtseyed if he found you unattractive. So many of the ladies started to bow their heads because they didn't want to see if he smiled at them.

Because Anne Marie is a Queen (even if former), whereas Harry and William are just Princes. Or, in other words, protocol, respect.
For the same reason, Kate curtseys to Crown Princess Margarita of Romania, Queen Anne Marie, and other royal ladies from former monarchies.

Current monarchies tend to be much more uptight when it comes to former royal houses; as far as they are concerned, once a King - always a King. You might have noticed how in the official portrait taken before the Lunch for Monarchs, former Sovereigns (Michael of Romania, Simeon of Bulgaria...) were given great prominence - greater, in fact, than reigning ones for they were seated immediately next to the Queen. That's because as far as Royal Families are concerned, Michael and Simeon have been Kings since 1927 (1940) and 1943 respectively, and the fact their countries are no longer monarchies is somewhat irrelevant.

As far as monarchies are concerned, they are. Have you noticed that the former Monarchs are addressed by their full titles and styles by virtually all current monarchies, and most other countries too? It's like being a marine; there is no such thing as "ex". Now, Crown Princess Margarita will never be Queen Margarita (unless monarchy in Romania is reinstated) because she didn't hold the title at the time monarchy in the country was abolished. Her father though will remain a King for the rest of his life.

As far as monarchies are concerned, they are. Have you noticed that the former Monarchs are addressed by their full titles and styles by virtually all current monarchies, and most other countries too? It's like being a marine; there is no such thing as "ex". Now, Crown Princess Margarita will never be Queen Margarita (unless monarchy in Romania is reinstated) because she didn't hold the title at the time monarchy in the country was abolished. Her father though will remain a King for the rest of his life.

I think the DOE was asking about real life. When the country you rule decides not to be ruled, no matter how illegal, unfair, usurper-ous, whatever - you no longer rule a country. There is some other legal platform that rules the country.

I do applaud fellow royals/ex-royals when they stand for monarchies that have been illegally, if factually, overthrown. But that does not necessarily incite the locals to take up arms and reinstate the monarchy.

I think the DOE was asking about real life. When the country you rule decides not to be ruled, no matter how illegal, unfair, usurper-ous, whatever - you no longer rule a country. There is some other legal platform that rules the country.

I do applaud fellow royals/ex-royals when they stand for monarchies that have been illegally, if factually, overthrown. But that does not necessarily incite the locals to take up arms and reinstate the monarchy.

I understand and fully agree with that; the people of Greece no longer recognise Constantine and Anne Marie as their King and Queen, so they are not legally monarchs of anything. I was explaining the situation from the point of view of monarchies as I understand it.

Well Americans still accord Jimmy Carter, George HW Bush, Bill Clinton and George W Bush the title of President even though they no longer hold office so there isn't much difference.

This habit has always amused me. Australians continue to accord our former Prime Ministers the same level of contempt accorded to them while they were in office. They're lucky to just get referred to as "Howard" or "Hawke" or "Keating" without some expletive in front of it. At best it's Mr, and that's only formally.